calculus

Use the demand function
X=325(1-(6p/7p+4)) to find the rate of change in the demand x for the given price p=$5.00. Round your answer to two decimal places.

A. 5.13 UNITS PER DOLLAR
B. -0.85 UNITS PER DOLLAR
C. 0.85 UNITS PER DOLLAR
D. 1.35 UNITS PER DOLLAR
E. -5.13 UNITS PER DOLLAR

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  1. Setting u(p) = 6p and v(p)=7p+4, we have x=325(1-u/v). So,

    dx/dp = -325 (uv'-u'v)/v^2
    = -325(6p(7)-6(7p+4)/(7p+4)^2
    = -325(42p-42p-24)/(7p+4)^2
    = 325*24/(7p+4)^2

    x'(5) = 32*24/39^2 = 5.13

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